Connections Between Stability, Convexity of Internal Energy, and the Second Law for Compressible Newtonian Fluids

2005 ◽  
Vol 72 (2) ◽  
pp. 299-300 ◽  
Author(s):  
Stephen E. Bechtel ◽  
Francis J. Rooney ◽  
M. Gregory Forest
Keyword(s):  
Convex Function ◽  
Bulk Modulus ◽  
Specific Heat ◽  
Internal Energy ◽  
Linear Stability ◽  
Specific Volume ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Isothermal Bulk Modulus ◽  
Rest State

In this note we provide proofs of the following statements for a compressible Newtonian fluid: (i) internal energy being a convex function of entropy and specific volume is equivalent to nonnegativity of both specific heat at constant volume and isothermal bulk modulus; (ii) convexity of internal energy together with the second law of thermodynamics imply linear stability of the rest state; and (iii) linear stability of the rest state together with the second law imply convexity of internal energy.

First and second laws of thermodynamics: relationship, “inconsistency”, hidden effects

2020 ◽  
pp. 63-73
Author(s):  
A. M. Savchenko ◽  
Yu. V. Konovalov ◽  
A. V. Laushkin
Keyword(s):  
Free Energy ◽  
Internal Energy ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Entropy Of Mixing ◽  
Ideal Mixing ◽  
Laws Of Thermodynamics ◽  
Relationship Of ◽  
The Relationship

The relationship of the first and second laws of thermodynamics based on their energy nature is considered. It is noted that the processes described by the second law of thermodynamics often take place hidden within the system, which makes it difficult to detect them. Nevertheless, even with ideal mixing, an increase in the internal energy of the system occurs, numerically equal to an increase in free energy. The largest contribution to the change in the value of free energy is made by the entropy of mixing, which has energy significance. The entropy of mixing can do the job, which is confirmed in particular by osmotic processes.

scholarly journals Entropy and the Second Law of Thermodynamics—The Nonequilibrium Perspective

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 793
Author(s):  
Henning Struchtrup
Keyword(s):  
Thermodynamic Equilibrium ◽  
Nonequilibrium Thermodynamics ◽  
Local Thermodynamic Equilibrium ◽  
Thermodynamic Temperature ◽  
Second Law Of Thermodynamics ◽  
Equilibrium States ◽  
Second Law ◽  
Rest State ◽  
The Stability

An alternative to the Carnot-Clausius approach for introducing entropy and the second law of thermodynamics is outlined that establishes entropy as a nonequilibrium property from the onset. Five simple observations lead to entropy for nonequilibrium and equilibrium states, and its balance. Thermodynamic temperature is identified, its positivity follows from the stability of the rest state. It is shown that the equations of engineering thermodynamics are valid for the case of local thermodynamic equilibrium, with inhomogeneous states. The main findings are accompanied by examples and additional discussion to firmly imbed classical and engineering thermodynamics into nonequilibrium thermodynamics.

scholarly journals Nature of Heat and Thermal Energy: From Caloric to Carnot’s Reflections, to Entropy, Exergy, Entransy and Beyond

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 584 ◽  
Author(s):  
Milivoje M. Kostic
Keyword(s):  
Energy Transfer ◽  
Internal Energy ◽  
Thermal Energy ◽  
Mechanical Energy ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Generalized Entropy ◽  
Critical Issues ◽  
Thermal Phenomena

The nature of thermal phenomena is still elusive and sometimes misconstrued. Starting from Lavoisier, who presumed that caloric as a weightless substance is conserved, to Sadi Carnot who erroneously assumed that work is extracted while caloric is conserved, to modern day researchers who argue that thermal energy is an indistinguishable part of internal energy, to the generalization of entropy and challengers of the Second Law of thermodynamics, the relevant thermal concepts are critically discussed here. Original reflections about the nature of thermo-mechanical energy transfer, classical and generalized entropy, exergy, and new entransy concept are reasoned and put in historical and contemporary contexts, with the objective of promoting further constructive debates and hopefully resolve some critical issues within the subtle thermal landscape.

scholarly journals The second law of thermodynamics as variation on a theme of Carathéodory

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210425
Author(s):  
Joe D. Goddard
Keyword(s):  
Energy Balance ◽  
State Space ◽  
Internal Energy ◽  
Second Law Of Thermodynamics ◽  
Irreversible Processes ◽  
Second Law ◽  
Classic Work ◽  
Axiomatic Foundation ◽  
Convexity Properties ◽  
Definition Of

This paper revisits the second law of thermodynamics via certain modifications of the axiomatic foundation provided by the celebrated 1909 work of Carathéodory. It is shown that his postulate of adiabatic inaccessibility represents one of several constraints on the energy balance that serve to establish the existence of thermostatic entropy as a foliation of state space, with temperature representing a force of constraint. To achieve the thermostatic version of the second law, as embodied in the postulates of Clausius and Gibbs, work principles are proposed to define thermostatic equilibrium and stability in terms of the convexity properties of internal energy, entropy and related thermostatic potentials. Comparisons are made with the classic work of Coleman and Noll on thermostatic equilibrium in simple continua, resulting in a few unresolved differences. Perhaps the most novel aspect of the current work is an extension to irreversible processes by means of a non-equilibrium entropy derived from recoverable work, which generalizes similar ideas in continuum viscoelasticity. This definition of entropy calls for certain revisions of modern theories of continuum thermomechanics by Coleman, Noll and others that are based on a generally inaccessible entropy and undefined temperature.

scholarly journals On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 930
Author(s):  
Corti
Keyword(s):  
Gravitational Field ◽  
Thermodynamic Properties ◽  
Internal Energy ◽  
Center Of Mass ◽  
Second Law Of Thermodynamics ◽  
Ideal Gas ◽  
Thermodynamic Efficiency ◽  
Second Law ◽  
Cyclic Process ◽  
Carnot Cycle

A reversible cyclic process is analyzed in which the center of mass of an ideal gas is raised in a gravitational field during both an expansion phase and a subsequent contraction phase, with the gas returning to its initial height in a final step. When the properties of the gas are taken as uniform, the thermodynamic efficiency of this cycle is able to exceed that of a corresponding Carnot cycle, which is a violation of the second law of thermodynamics. The source of this discrepancy was previously claimed, when analyzing a similar heating and cooling of a sphere, to be the assumed independence of the internal energy on the gravitational field. However, this violation is only apparent since all of the effects of the gravitational field were not incorporated fully into the thermodynamic analysis of the cycle. When all the influences of the gravitational field are considered, no possible violation of the second law can occur. The evaluation of the entropy changes of the gas throughout the cycle also highlights other key inconsistencies that arise when the full effects of the gravitational field are neglected. As the analysis of the cycle provided here shows, the assumption of the independence of the internal energy, as well as other thermodynamic properties, on the gravitational field strength can still be invoked.

The Analogical Turn (1884–1887)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Boltzmann Equation ◽  
Statistical Mechanics ◽  
Mechanical System ◽  
Thermal Equilibrium ◽  
Special Kind ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Equipartition Theorem ◽  
Royal Road ◽  
H Theorem

This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to relate thermodynamics to mechanics, including the kinetic-molecular analogy, into a family of partial analogies all derivable from what we would now call a microcanonical ensemble. At that time, Boltzmann regarded ensemble-based statistical mechanics as the royal road to the laws of thermal equilibrium (as we now do). In the same period, he returned to the Boltzmann equation and the H theorem in reply to Peter Guthrie Tait’s attack on the equipartition theorem. He also made a non-technical survey of the second law of thermodynamics seen as a law of probability increase.

First and Second Law Analysis of a Flat Plate Collector Working With Nanofluids

2018 ◽  
Author(s):  
M. T. Nitsas ◽  
I. P. Koronaki ◽  
L. Prentza
Keyword(s):  
Flat Plate ◽  
Second Law Of Thermodynamics ◽  
Climatic Conditions ◽  
Working Fluid ◽  
Second Law ◽  
Inlet Temperature ◽  
Water Tank ◽  
Systems Quality ◽  
Typical Day ◽  
Flat Plate Collector

The utilization of solar energy in thermal energy systems was and always be one of the most effective alternative to conventional energy resources. Energy efficiency is widely used as one of the most important parameters in order to evaluate and compare thermal systems including solar collectors. Nevertheless, the first law of thermodynamics is not solely capable of describing the quantitative and qualitative performance of such systems and thus exergy efficiency is used so as to introduce the systems’ quality. In this work, the performance of a flat plate solar collector using water based nanofluids of different nanoparticle types as a working fluid is analyzed theoretically under the climatic conditions in Greece based on the First and Second Law of Thermodynamics. A mathematical model is built and the model equations are solved iteratively in a MATLAB code. The energy and exergy efficiencies as well as the collector losses coefficient for various parameters such as the inlet temperature, the particles concentration and type are determined. Moreover, a dynamic model is built so as to determine the performance of a flat plate collector working with nanofluids and the useful energy that can be stored in a water tank. The exergy destruction and exergy leakage are determined for a typical day in summer during which high temperatures and solar intensity values are common for the Greek climate.

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